Recall that the diameter [1]} of a connected graph is the length of the "longest shortest path" between two vertices of the graph. Thus, the diameter of \(\text{Cay}(G, S)\)  is an upper bound of distance \(d(\sigma , I)\)  from an arbitrary vertex \(\sigma \)  to vertex \(I\)  in \(\text{Cay}(G, S)\) , where the computation of \(d(\sigma , I)\)  is obtained by sorting permutation \(\sigma \)  to the identity permutation \(I\)  in \(G\)  by means of the minimum generator sequence using the generating set \(S\)  [2]}. Thus, the diameter of \(\text{Cay}(G, S)\)  is an upper bound of the lengths of minimum generator sequences for permutations in \(G\)  using the generating set \(S\)  [3]}.
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